Optimization Analysis of a 2D Magnetic Cloaking Problem for Bilayer Structure

Abstract

We consider the control problems for the 2D model of magnetic scattering by a permeable isotropic obstacle having the form of a cylindrical bilayer. These problems arise while developing the design technologies of magnetic cloaking bilayer devices using the optimization method for solving the corresponding inverse problems. The solvability of direct and optimization problems for the magnetic scattering model under study is proved. The optimality system which describes the necessary conditions of extremum is derived. Based on its analysis the sufficient conditions to the data are established which provide local uniqueness and stability of optimal solutions. Also numerical aspects of applying the optimization approach are discussed.